Chemical mechanical polishing apparatuses (CMP apparatuses) are commonly used for the planarization of silicon wafers. In one type of CMP apparatus, a rotating pad is placed in contact with a rotating wafer and the pad is moved back and forth laterally relative to the rotating wafer. Additionally, a polishing slurry is forced into a gap between the wafer and the pad. The slurry is typically an aqueous solution that carries a high concentration of nanoscale abrasive particles. The slurry can play a number of critical roles in the polishing of the wafer. For example, the chemical composition of the slurry can alter the surface properties of the wafer, soften the wafer surface and make it amenable to material removal. Further, the abrasive particles in the slurry remove material from the wafer surface by cutting nanoscale grooves in the wafer surface.
Some in the industry believe that most of the material removal occurs when pad asperities on the pad are in contact with the wafer, trapping slurry particles between them. The asperities push the particles into the wafer surface and drag them along so the abrasive particles act as nanoscale cutting tools. Slurry particles dragged along the wafer by fluid friction probably contribute, at most, a small fraction of the overall material removal.
Designers are constantly trying to improve the accuracy and efficiency of CMP apparatuses. For example, if the material removal rate of the pad can be accurately calculated for a range of configurations, the movement of the pad, the rotation rate of the pad, the pressure applied by the pad, the rotation rate of the wafer, the design of the pad, the location of the inlets for the slurry and/or the rate of slurry flow can be adjusted and controlled to improve accuracy and efficiency.
Unfortunately, a number of factors are believed to influence the material removal rate of the CMP apparatus. Some of these factors can not be quickly and accurately calculated. Other factors are currently not exactly known. Accordingly, designers have not been able to accurately calculate the material removal rate of CMP apparatuses for a range of configurations.
In light of the above, there is a need for a system and method for accurately calculating one or more of the factors that may influence the material removal rate. Additionally, there is a need for a system and method that can accurately calculate slurry flow in the gap and pressure of the slurry in the gap for a range of configurations. Further, there is a need for a new polishing rate model that takes in account a freshness of the slurry supplied to a given region of the polishing pad. Moreover, there is a need for a polishing apparatus that quickly and accurately polishes a substrate such as semiconductor wafers.